What are the differences between white and this darkroom red/orange active autofocus assistance lights?
AF assist (if that's what you're referring to) is simply a way to illuminate a dark subject to help the camera focus. The colour of the light isn't really important - what's more important is that it (a) is bright enough to allow the camera to focus (b) doesn't adversely affect the metering and (c) is efficient in terms of battery use. A red LED would seem to be the best way to meet all these criteria, which is why it is the most common kind. Of course LED technology is improving all the time, which may explain why some cameras can get away with a green beam.
I think it doesn't really matter; as several people have commented, these lights come in all sorts of colors. And some cameras without dedicated AF assist lights strobe the flash itself rapidly for AF assist. The first practical LEDs were red, and at least up until recently if not still today, it's easier and cheaper to make red LEDs very bright. That's probably why many AF assist lights are red.
The idea that red might be best for recognizing contours is new to me, and any information you have on that would be welcome over in my question on human color vision and photography. But, I do know that red light is often used where it is important to preserve night vision. This is because of the mechanism by which we adjust from day to night vision. There's a chemical called rhodopsin which is vital for night vision, and this is bleached-out by bright light — taking about half an hour to regenerate. That's why it takes a while to adjust to the dark. Red light (because it's less energetic, perhaps, or perhaps for some other reason — I'm not really sure of the chemistry) is less destructive to rhodopsin, so your night-adapted vision isn't reset.
It's possible that camera-makers are thinking of this when they chose red AF assist lights, but my guess is they were thinking more of the pocketbook. I suppose, if I did a lot of night shooting and had the choice, I'd have a preference for red.
(For the same reason, I prefer red for the display of my bedroom alarm clock, but as everyone moves to backlit LCD screens, this is getting harder and harder to find. A shame!)
A white focus assist light has the best chances of reflecting back from any surface; a red one will have harder time aiding focusing on colors that have little red in them (e.g. green leaves).
Some traffic cameras use red flash to avoid dazzling drivers; similarly, a red focus assist light is less likely to make subjects squint, or even notice the photographer.
A red LED is significantly cheaper than a white LED.